Messrs. John E. Tracy, of Milwaukee, Wis., and W. D. McHugh, of Omaha, Neb., for appellee.

Mr. Justice BRANDEIS delivered the opinion of the Court.

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The Constitution of Michigan (article 12, § 7) authorizes the Legislature to pass laws establishing 'reasonable maximum rates or charges for the transportation of passengers and freight.' In 1907 it fixed two cents a mile as the maximum intrastate passenger fare on railroads operating in the Lower Peninsula and three cents for those in the upper. By act approved May 2, 1911 (Public Laws No. 276), the two-cent rate was made applicable to all the railroads of the state whose gross earnings on passenger trains equal or exceed $1,200 per mile of line operated. Before the statute took effect, the Duluth, South Shore & Atlantic Railway Company, an interstate carrier operating in the Upper Peninsula, brought this suit in the District Court of the United States for the Eastern District of Michigan to enjoin the enforcement of the act. The bill alleged that the reduced rate would deprive plaintiff of its property without due process of law in violation of the Fourteenth Amendment. The Attorney General and the railroad commissioners of the state, being charged by the law with its enforcement, were made defendants. They denied that the rate was confiscatory; and on this issue the District Court found for the railway. A final decree granting the relief sought was filed February 14, 1918, and an appeal to this court was promptly applied for by the defendants and allowed. Meanwhile, on January 1, 1918, the federal government had taken over the operation of this and other railroads, and is still operating the same. The two-cent rate was never put into effect on this railroad, as a restraining order issued upon the filing of the bill was continued until entry of the final decree. In 1919 the statute attacked here was repealed (Michigan Public Laws No. 382). But the case has not become moot for the following reason: On continuing the restraining order the railway was required to issue to all intrastate passengers receipts by which it agreed to refund, if the act should be held valid, the amount paid in excess of a two-cent fare. Later the railway was required to deposit, subject to the order of the court, such amounts thereafter collected. The fund now on deposit exceeds $800,000, and the refund coupons are still outstanding. In order to determine the rights of coupon holders and to dispose of this fund it is necessary to decide whether the act of 1911 was, as respects this railroad, confiscatory.

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The issues of fact were tried below with great thoroughness. The case was referred to a special master to hear the proofs and to report the evidence together with his findings to the court. The report fills 503 pages of the printed record. The transcript of the testimony introduced before him covered more than 12,000 typewritten pages; and there were besides many exhibits. The evidence before the master related largely to the results of the operation of the railroad for the four years ending June 30, 1913. When the case came on for hearing before the District Judge in 1917, supplemental evidence was taken in open court covering the operations of the four additional years ending June 30, 1917. The evidence disclosed the usual diversity of opinion as to the value of the property and as to the proper method of dividing between the passenger and freight services the common expenses and the charges for property used in common. Upon the whole evidence the court found that the two-cent fare would have resulted in a return on intrastate passenger business of less than 2 per cent. during the six years ending June 30, 1917.

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Between the commencement of this suit and the entry of the final decree many of the questions in controversy below have been settled by the decisions of this Court in other cases.1 The state officials do not deny that there was legal evidence to justify the findings of fact made by the lower court; nor do they request that this court should undertake a general review of the evidence. But they insist that the finding of the district judge of the low return is erroneous, and that the error is due partly to his having included in his calculations property and operations which should have been excluded, and partly to his having adopted improper formulas for the division of common charges and expenses as between the freight and the passenger services; and that if these specific errors are corrected it will appear that the two-cent fare would have been highly remunerative. These alleged errors must be considered separately.

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First. It is contended that the Western Division should be excluded from the calculation. The Duluth, South Shore & Atlantic Railway extends from Sault Ste. Marie to Duluth and has, including branches, 584 miles of line, 475 of which are in Michigan. The Eastern Division serves mainly the iron region; the Central, the copper country; the Western, extending through sparsely settled country from Nestoria, Mich., 101 miles to the Wisconsin state line, and thence to Duluth, serves mainly interstate business. This division is said to have been built not in a desire to serve local needs, but for the purpose of establishing a through line from Duluth to Sault Ste. Marie. The statement, if true, furnishes no reason for excluding it from the calculation. The cost per mile of transporting passengers varies greatly on different parts of the same railroad system according to circumstances, being dependent, among other things, upon the cost of the roadbed and terminals, the grade, the number and character of the trains, the density of traffic and the length of the haul. The justification for a uniform fare per mile is furnished by the doctrine of averages; and the Legislature of Michigan made clear its purpose to apply the doctrine of averages in order to give to travelers the benefit of the two-cent fare on those portions of a railroad on which travel was light and the cost of carrying each passenger necessarily far in excess of two cents a mile. For this act declares:

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'That in computing the passenger earnings per mile of any company the earnings and mileage of all branch roads owned, leased, controlled or occupied or that may hereafter be owned, leased, controlled or occupied by such company * * * shall be included in the computation [i. e., determining whether the year's gross passenger earnings equal $1,200 per mile], and the rate of fare shall be the same on all lines owned, leased, controlled or occupied by such company.'

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In other words, the Legislature has declared that for the purpose of determining the right of an intrastate passenger to travel on any part of the company's lines at the rate of two cents a mile, all of the lines within the state must be treated as one; that those on which travel is light must be averaged with those on which it is dense; and obviously also that those parts of the system which are unprofitable must be taken with those which are profitable. Every part of the railroad system over which the passenger is entitled by the act to ride for a two-cent fare must be included in the computation undertaken to determine whether the prescribed rate is confiscatory. This is true, at least, in the absence of illegality or mismanagement in the acquisition or operation of the division in question; and of such there is not even a suggestion in the record. There is nothing in San Diego Land & Town Co. v. National City, 174 U. S. 739, 758, 19 Sup. Ct. 804, 43 L. Ed. 1154, or in San Diego Land & Town Co. v. Jasper, 189 U. S. 439, 446, 23 Sup. Ct. 571, 47 L. Ed. 892, upon which the state officials rely, which is inconsistent with this conclusion.

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Second. It is likewise contended that the so-called South Line between Marquette and Ishpeming should be excluded from the calculation. This line which for miles substantially parallels the main line, was originally built as an independent road and was purchased by plaintiff's predecessor in 1884 probably to avoid ruinous competition. It is used mainly for heavy freight, and the intrastate passenger travel over it is light. It is asserted that the construction of this road was not required to supply the transportation needs, and that it would still be possible to carry all existing traffic between Marquette and Ishpeming over the main line. What has been said above in regard to the Western Division applies equally to the South Line.

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Third. It is contended also that a loss was incurred in operating through passenger trains from Houghton over the Mineral Range Railroad to Calumet and that such loss should be excluded from this calculation. This extension of plaintiff's service was clearly reasonable in view of the importance of Calumet, which lies only fourteen miles from its own lines. It was admitted by the state officials that passengers on the route were, under the act, entitled to travel at the two-cent rate. The fact that the service was furnished by acquiring traffic rights instead of by building an independent line, clearly affords no reason for excluding the results of the operation from the calculation.

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Fourth. The further contention is made that the sleeping car, parlor car and dining car services should be treated as separate operations; that they should be charged with their proportion of specific and general expenses but credited only with the amounts received from charges for the specific service; and that no part of the apparent loss on these services should be taken into consideration in determining whether the two-cent fare is confiscatory. In support of this contention it is urged that these services were voluntary; that the law (Michigan Public Acts of 1875, No. 38) permits railroads to make special charges for these services 'in addition to the regular passenger fares allowed by law,' and that travelers in day coaches must not be allowed to suffer because a railroad fails to make these services compensatory. On American railroads of importance these services have been well-nigh universal for more than a generation; and the charges for them are substantially uniform throughout the country. It would be practically impossible, as it would be obviously unwise, for a railroad like the plaintiff's either to discontinue the services or to increase the charges to cover the cost of the particular service on its line. It is inconceivable that the Legislature of Michigan should have intended in enacting the two-cent fare law to deny to its citizens these customary facilities; and for the purpose of determining whether the act is confiscatory the passenger service including these facilities must be treated as a whole. The fact alleged that these facilities are used mainly by interstate travelers is immaterial.

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Fifth. The remaining objection relates to the formula adopted by the lower court for dividing charges and expenses common to freight and passenger services, and not capable of direct allocation. What method should be pursued in making such division is a very difficult problem to which railroad accountants, the Interstate Commerce Commission and state Railroad Commissions have for years given serious attention.2 Despite much patient study and the exhibition of great ingenuity no wholly satisfactory method has yet been devised. The variables due to local conditions are numerous; and experience teaches us that it is much easier to reject formulas presented as being misleading than to find one apparently adequate. The science of railroad accounting is in this respect in process of development; and it may be long before a formula is devised which can be accepted as satisfactory. For the present, at least, the question what formula the trial court should adopt presents a question, not of law, but of fact; and we are clearly unable to say that the lower court erred in adopting the method there pursued.3

The average rate of return for the years 1914-1917 according to the formula adopted by the trial judge was 1.20 per cent. By the use of a formula more favorable to the defendant he found it to be 2.52 per cent. The modified revenue train mile ratio used by the plaintiff showed a loss of over $100,000 a year; while the gross ton mile ratio proposed by the defendant indicated an average return of at most 5.82 per cent. Of these methods employed by the parties it may be noted that the Interstate Commerce Commission has said:

'The representatives of the state commissions advocated the use of 'gross ton miles' as a basis, while the representatives of the railways favored 'engine ton miles.' The discussion seemed to be somewhat influenced by the possible effect of these respective bases on statistical evidence which might be introduced in passenger rate cases. It may fairly be said that the facts and arguments presented do not warrant the final approval by the Commission of either the gross ton mile or the locomotive ton mile at this time.' Rules Governing the Separation of Operating Expenses Between Freight Service and Passenger Service on Large Steam Railways, Effective July 1, 1915, p. 3. These rules are now in process of revision.